The 22-year-old has yet to play a first-team game for the Eindhoven club but has impressed during two seasons on loan with RKC Waalwijk. He made 33 and 34 appearances for the club in the two seasons
Zoet is first-choice keeper for the Netherlands Under-21 side, and helped the Dutch youngsters on their way to a semi-final place before late defeat to eventual runners-up Italy.
If he moves to St James' Park he is likely to provide backup for Tim Krul and Rob Elliot, with Steve Harper having left the club in the summer.
The Zoet deal is believed to have been set up by Joe Kinnear, the new director of football at Newcastle.